The interplay between crystalline symmetries and band topology drives exotic states in materials, which have been investigated intensively over the years for their attributes to experimental standouts [1]}, [2]}, [3]}, [4]}. Dirac and Weyl fermions predicted as the fundamental particles in high-energy physics have been reported to exist as low-energy excitations in topological quantum materials [5]}, [6]}, [7]}, [8]}. Four-fold degenerate nodes in Dirac semimetals are theoretically predicted and subsequently realized in experiments. The energy dispersion near Dirac nodes is linear in all three spatial directions that mimic the Dirac equation with a net-zero chiral charge. These Dirac points are protected by a combination of inversion, time-reversal, and lattice symmetries. By breaking either inversion or time-reversal, a Dirac node splits into two opposite charged Weyl points where energy dispersion is described by the chiral Weyl equation [9]}, [10]}, [11]}, [12]}. Chirality, degeneracy, and dimensionality of the crossing points distinguish numerous topological states in materials [13]}, [14]}, [15]}.
Non-symmorphic symmetries can impose band crossings at high symmetry points in the Brillouin zone (BZ) and produce higher-fold fermions without any high-energy analogue. Specifically, cubic systems of space group \(P2_13\)  (\(\#198)\)  such as \(\rm Rh(Si, Ge)\) , \(\rm (Pd, Pt)Ga\)  etc. evince non-symmorphic symmetry protected multifold fermions at the high symmetry points with unconventional low-energy excitations called spin-\(\frac{3}{2}\)  Rarita-Schwinger fermions  [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}. The multifold chiral fermions produce novel optoelectronic responses such as the photogalvonic effect [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}. In this work, we have investigated the topological quantum properties of single crystals of chiral material \(\rm PtAl\)  combining theoretical analysis and experimental magnetotransport measurements. Hall resistivity measurements revealed that the electrons dominate over hole carriers in the field range \(0-14\)  T and in the temperature range \(1.8 - 100\)  K. The Berry phase is estimated from the de Haas-van Alphen (dHvA) oscillations. Linear \(\alpha \)  and parabolic \(\beta \)  bands are observed at \(\Gamma \)  high symmetry point possessing non-trivial and trivial Berry phases, respectively. The first-principles calculations reveal the three- and four-fold nodal points at \(\Gamma \)  and \(R\)  time-reversal invariant momentum (TRIM) points near the Fermi level without spin-orbit coupling. In the presence of spin-orbit coupling, the nodal crossings at \(\Gamma \)  and \(R\)  points evolve into the four-fold and six-fold degenerate nodal point containing low energy excitations as the Rarita-Schwinger fermions. We also calculate the optical response, which reveals that optical conductivity is almost linear with frequency in the energy range from 400 to 800 meV suggesting the linear band transitions from the near Fermi energy bands. Unconventional electronic and optical properties show that PtAl is an interesting chiral material for investigating topological properties and device applications.
